Existence of an attractor and Horseshoe in multidimensional H\'{e}non map

TL;DR

This paper proves the existence of attractors and Smale horseshoes in multidimensional Hénon-like maps using auxiliary maps, analyzing complex attractor structures for small coupling parameters.

Contribution

It provides new sufficient conditions for the existence of topological Smale horseshoes in multidimensional Hénon-like maps with quadratic and cubic nonlinearities.

Findings

Existence of trapping domains containing attractors established.

Conditions for Smale horseshoes in quadratic and cubic cases derived.

Analysis of attractor complexity for small coupling parameters.

Abstract

In this paper using approach of 1-D auxiliary maps we prove the existence of trapping domains containing attractors of the multidimensional Henon-like maps. For both of quadratic and cubic nonlinearities we obtain sufficient conditions of topological Smale horseshoes existence. The complex structure of attractors is discussed in the case of small coupling parameter.